A367811 - OEIS

%I #16 Dec 21 2023 15:16:45

%S 1,10,2,12,11,13,14,15,16,17,18,19,20,120,3,21,121,22,122,23,123,24,

%T 124,25,125,26,126,27,127,28,128,29,129,30,130,100,31,131,101,32,132,

%U 102,33,133,103,34,134,104,35,135,105,36,136,106,37,137,107,38,138,108,39,139,109,119,110,111,112,113

%N Lexicographically earliest sequence of distinct positive terms such that the Levenshtein distance (Ld) between a(n) and a(n+1) is equal to the first digit of a(n+1).

%H Éric Angelini, <a href="https://cinquantesignes.blogspot.com/2023/12/more-levenshtein-distances.html">More Levenshtein distances</a>, Personal blog, December 2023.

%e a(1) =  1 and a(2) = 10 are separated by an Ld of 1, and 1 is the 1st digit of a(2)

%e a(2) = 10 and a(3) =  2 are separated by an Ld of 2, and 2 is the 1st digit of a(3)

%e a(3) =  2 and a(4) = 12 are separated by an Ld of 1, and 1 is the 1st digit of a(4)

%e a(4) = 12 and a(5) = 11 are separated by an Ld of 1, and 1 is the 1st digit of a(5)

%e a(5) = 11 and a(6) = 13 are separated by an Ld of 1, and 1 is the 1st digit of a(6) etc.

%t a[1]=1;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n-1],k]||EditDistance[ToString@a[n-1],ToString@k]!=First@IntegerDigits@k,k++];k);Array[a,68]

%o (Python)

%o from itertools import islice

%o from Levenshtein import distance as Ld

%o def agen(): # generator of terms

%o     an, aset, mink = 1, {1}, 2

%o     while True:

%o         yield an

%o         s, k = str(an), mink

%o         while k in aset or Ld(s, sk:=str(k)) != int(sk[0]): k += 1

%o         an = k

%o         aset.add(k)

%o         while mink in aset: mink += 1

%o print(list(islice(agen(), 68))) # _Michael S. Branicky_, Dec 01 2023

%Y Cf. A367810.

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Dec 01 2023